What is the rate law for the reaction 2A + 2B + 2C →→ products Initial [A] 0.273 Initial [C] Initial (B] 0.763 rate 0.400 3.0 0.819 0.273 0.273 0.763 1.526 0,763 0.400 9.0 0.400 12.0 0.800 6.0
What is the rate law for the reaction 2A + 2B + 2C →→ products Initial [A] 0.273 Initial [C] Initial (B] 0.763 rate 0.400 3.0 0.819 0.273 0.273 0.763 1.526 0,763 0.400 9.0 0.400 12.0 0.800 6.0
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![### Rate Law Determination for the Reaction 2A + 2B + 2C ➔ Products
To determine the rate law for this chemical reaction, we analyze the initial concentrations of reactants A, B, and C, alongside the observed reaction rates.
| Initial [A] | Initial [B] | Initial [C] | Rate |
|-------------|-------------|-------------|------|
| 0.273 | 0.763 | 0.400 | 3.0 |
| 0.819 | 0.763 | 0.400 | 9.0 |
| 0.273 | 1.526 | 0.400 | 12.0 |
| 0.273 | 0.763 | 0.800 | 6.0 |
---
**Analysis:**
1. **Effect of [A] on Rate:**
- Compare trials 1 and 2. When [A] changes from 0.273 to 0.819 (tripling), the rate increases from 3.0 to 9.0 (tripling).
- This suggests that the reaction rate is first-order with respect to A.
2. **Effect of [B] on Rate:**
- Compare trials 1 and 3. When [B] changes from 0.763 to 1.526 (doubling), the rate increases from 3.0 to 12.0 (quadrupling).
- This suggests that the reaction rate is second-order with respect to B.
3. **Effect of [C] on Rate:**
- Compare trials 1 and 4. When [C] changes from 0.400 to 0.800 (doubling), the rate increases from 3.0 to 6.0 (doubling).
- This suggests that the reaction rate is first-order with respect to C.
---
**Proposed Rate Law:**
\[ \text{Rate} = k [A]^1 [B]^2 [C]^1 \]
Where `k` is the rate constant for the reaction. This rate law suggests that the reaction is first-order with respect to A and C, and second-order with respect to B.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F437a6243-7f54-47cd-8dab-1c18de80702c%2F143bd18f-132c-49c8-b95c-4be0cd29d997%2Fiakcua_processed.png&w=3840&q=75)
Transcribed Image Text:### Rate Law Determination for the Reaction 2A + 2B + 2C ➔ Products
To determine the rate law for this chemical reaction, we analyze the initial concentrations of reactants A, B, and C, alongside the observed reaction rates.
| Initial [A] | Initial [B] | Initial [C] | Rate |
|-------------|-------------|-------------|------|
| 0.273 | 0.763 | 0.400 | 3.0 |
| 0.819 | 0.763 | 0.400 | 9.0 |
| 0.273 | 1.526 | 0.400 | 12.0 |
| 0.273 | 0.763 | 0.800 | 6.0 |
---
**Analysis:**
1. **Effect of [A] on Rate:**
- Compare trials 1 and 2. When [A] changes from 0.273 to 0.819 (tripling), the rate increases from 3.0 to 9.0 (tripling).
- This suggests that the reaction rate is first-order with respect to A.
2. **Effect of [B] on Rate:**
- Compare trials 1 and 3. When [B] changes from 0.763 to 1.526 (doubling), the rate increases from 3.0 to 12.0 (quadrupling).
- This suggests that the reaction rate is second-order with respect to B.
3. **Effect of [C] on Rate:**
- Compare trials 1 and 4. When [C] changes from 0.400 to 0.800 (doubling), the rate increases from 3.0 to 6.0 (doubling).
- This suggests that the reaction rate is first-order with respect to C.
---
**Proposed Rate Law:**
\[ \text{Rate} = k [A]^1 [B]^2 [C]^1 \]
Where `k` is the rate constant for the reaction. This rate law suggests that the reaction is first-order with respect to A and C, and second-order with respect to B.
![**Determining the Rate Constant of the Reaction**
**Reaction:**
\[ 2\text{NO}(g) + \text{Cl}_2(g) \rightarrow 2\text{NOCl}(g) \]
**Experimental Data:**
| Experiment | \([\text{NO}]\) (M) | \([\text{Cl}_2]\) (M) | Rate (M/s) |
|------------|-------------------|-------------------|------------|
| 1 | 0.0300 | 0.0100 | \(3.4 \times 10^{-4}\) |
| 2 | 0.0150 | 0.0100 | \(8.5 \times 10^{-5}\) |
| 3 | 0.0150 | 0.0400 | \(3.4 \times 10^{-4}\) |
**Choices for the Rate Constant (\(k\)):**
- a. \(1.13 \, \text{M}^{-2}\text{s}^{-1}\)
- b. \(9.44 \, \text{M}^{-2}\text{s}^{-1}\)
- c. \(59.6 \, \text{M}^{-2}\text{s}^{-1}\)
- d. \(0.0265 \, \text{M}^{-2}\text{s}^{-1}\)
- e. \(59.6 \, \text{M}^{-2}\text{s}^{-1}\)
**Explanation:**
To determine the rate constant (\(k\)), use the rate law:
\[
\text{Rate} = k [\text{NO}]^m [\text{Cl}_2]^n
\]
By comparing experiments, the values of \(m\) and \(n\) can be deduced, and consequently, \(k\) can be calculated by rearranging the rate law and solving with the provided data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F437a6243-7f54-47cd-8dab-1c18de80702c%2F143bd18f-132c-49c8-b95c-4be0cd29d997%2Foiwtt6r_processed.png&w=3840&q=75)
Transcribed Image Text:**Determining the Rate Constant of the Reaction**
**Reaction:**
\[ 2\text{NO}(g) + \text{Cl}_2(g) \rightarrow 2\text{NOCl}(g) \]
**Experimental Data:**
| Experiment | \([\text{NO}]\) (M) | \([\text{Cl}_2]\) (M) | Rate (M/s) |
|------------|-------------------|-------------------|------------|
| 1 | 0.0300 | 0.0100 | \(3.4 \times 10^{-4}\) |
| 2 | 0.0150 | 0.0100 | \(8.5 \times 10^{-5}\) |
| 3 | 0.0150 | 0.0400 | \(3.4 \times 10^{-4}\) |
**Choices for the Rate Constant (\(k\)):**
- a. \(1.13 \, \text{M}^{-2}\text{s}^{-1}\)
- b. \(9.44 \, \text{M}^{-2}\text{s}^{-1}\)
- c. \(59.6 \, \text{M}^{-2}\text{s}^{-1}\)
- d. \(0.0265 \, \text{M}^{-2}\text{s}^{-1}\)
- e. \(59.6 \, \text{M}^{-2}\text{s}^{-1}\)
**Explanation:**
To determine the rate constant (\(k\)), use the rate law:
\[
\text{Rate} = k [\text{NO}]^m [\text{Cl}_2]^n
\]
By comparing experiments, the values of \(m\) and \(n\) can be deduced, and consequently, \(k\) can be calculated by rearranging the rate law and solving with the provided data.
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